Parameters that promote rapid formation of aligned high-T_c phase in the high-temperature superconductor (Bi,Pb)₂Sr₂Ca₂Cu₃O_x (Bi-2223) powder in tube superconducting tapes have been studied. A rapid phase formation was achieved by two means. Firstly, frequent mechanical pressings during the early stages of the heat treatment were applied. The pressings counteract the expansion that occurs during sintering, increase grain connectivity and reduce diffusion distances. Secondly, the fraction of process time within the thermodynamically stable region of the Bi-2223 phase was maximized by ramping of the oxygen partial pressure during heating and cooling. In addition, the starting phase composition of the superconductor powder was found to have a critical influence on the reaction speed. A complex phase composition gave the fastest formation rate of Bi-2223 phase. Within 30 h of processing time, critical current densities exceeding 12 kA cm^-2 (1 mu V cm^-1, 77 K, 0 T) were obtained compared to 2-4 kA cm^-2 without the above measures. Also, the effect of variations in oxygen partial pressure, pressing schedules, partial melting and a two-component starting powder based on (Bi,Pb)₂Sr₂CaCu₂O_x were investigated for this process.